Entropy production strength

Entropy production strength. We will derive the expression for a. Consider a small volume element AxAyAz within a given system. The entropy balance for this volume element can be stated as 

Let s denote the specific entropy (that is, entropy per unit mass), and J the entropy flux per unit time per unit surface area then 

Equation (2.65) is similar to any other balance expression, with the difference that there is a source term representing the production of ertropy. A different form of the above equation can be presented in. of total derivative of s  

the total entropy flux 7 consists of three parts (1) (2) and (3) psv which represent the contributions 

V re S, U, and V are the total entropy, internal energy, and volume, actively, and is the total mass of component i. Note that in the above equation, the chemical potential is defined as /q = (dU/dni)g y the molecular weight of component i, Mi, appears to make the chemical potential stay the same as defined in Chapter 1. The extensive quantities S, U, and V can be expressed in terms of specific quantities (quantity per unit mass) S — ms, U = mu, and V — mv, where m — mi. If we assume m = 1 in Eq. (2.68) and divide by dt, 

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The entropy source strength < > is the rate of entropy production per unit volume... 

The product of the entropy source strength and the absolute temperature is called the dissipation function 4 ... 

From Eqs. (3.118), (3.137), and (3.138), the entropy source strength or the rate of local entropy production per unit volume < > is defined by... 

The rate of entropy production is obtained from the local value of entropy production or entropy source strength d>... 

A central quantity of this treatment is the entropy production, a(r, t). The entropy density, in contrast with the previous extensive property densities, is not conserved. To obtain an expression for the entropy production one has to postulate a local version of the Gibbs relation (the second law of thermodynamics) r d5 = dU + pdV. After some manipulations the entropy source strength can be given as ... 

It is important to emphasize the role of the solid state in providing a medium for the formation of the molecular assembly 2(resorcinol) 2(4,4 -bpe). Indeed, that 2(resorcinol) 2(4,4 -bpe) is stabilized by weak forces (i.e. hydrogen bonds) comparable in strength to structure effects of solvent and entropy of the liquid phase [13] means that the components of 2(resorcinol)-2(4,4 -bpe) may assemble in solution to produce multiple equilibria involving individual molecules and undesirable (photostable) complexes. In effect, the solid state was used to sequester [23] 2(resorcinol) 2(4,4 -bpe) from the liquid phase, facilitating the formation of the desired photoactive complex and construction of the cyclobutane product. 

Entropy dominates equilibrium constants in the difference between inter- and intramolecular reactions. In Chapter 6 we explained that hcmiacetal formation is unfavourable because the C=0 double bond is more stable than two C-0 single bonds. This is clearly an enthalpy factor depending simply on bond strength. That entropy also plays a part can be clearly seen in favourable intramolecular hemiacetal formation of hydroxyaldehydes. The total number of carbon atoms in the two systems is the same, the bond strengths are the same and yet the equilibria favour the reagents (MeCHO + EtOH) in the inter- and the product (the cyclic hemiacetal) in the intramolecular case. 

When differences between Af5, ° of reactants and products are taken the entropies of the elements cancel. In the calculations here we will use the first form of equation 15.7-1. Since the functions Af5, ° for reactants in an enzyme-catalyzed reaction can be added and subtracted, the complicated function for the reaction can be used to calculate A,5 ° at specified temperature, pH, and ionic strength. 

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